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Report on experiments with tube-bulging machine

Campa, Tadej

Published: 01/01/1995

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Citation for published version (APA):Campa, T. (1995). Report on experiments with tube-bulging machine. (TU Eindhoven. Fac. Werktuigbouwkunde,Vakgroep WPA : rapporten). Eindhoven: Technische Universiteit Eindhoven.

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Technische Universiteit Eindhoven Faculteit Werktuigbouwkunde Vakgroep Produktietechnologie en Automatisering


Tadej Campa

April 1995 WPA 120031

ABSTRACT _____________________________________________ 2

PREFACE 2

1. LIST OF SYMBOLS 3

1. HYDROFORMING 4 1.1 TUBE-BULGING 4 1.2 THE GOAL OF THE RESEARCH 4

2. THE SYSTEM 5 2.1 HOW THE SYSTEM WORKS 5 2.2 FLUCTUATIONS OF THE DATA 5 2.3 SUDDEN JUMP 6 2.4 SERIES OF CONSTANT VALUES 6 2.5 DISAGREEMENT AMONG SENT DATA AND RECEIVED DATA 7 2.6 DIFFERENT SPEED RATE AT CHANGING PRESSURE AND FORCE 7 2.7 BURSTING 8 2.8 RESET AFTER EACH SET OF MEASURED VALUES 8

3. THE MODEL 8 3.1 DIFFERENT RESULTS AS EXPECTED 11 3.2 CORRECTING THE SEALING FORCE 11 3.3 DESCRIPTION OF THE SPECIMENS 12 3.4 RESULTS 12 3.5 DETERMINING REAL ex. 14 3.6 EXACTNESS OF REAL ex. 14 3.7 WALL THICKNESS 15

4. THE CONCLUSION 16

5. ACKNOWLEDGEMENT 17

6. LITERATURE LIST 18

ITadej Campa 1 WPA-TUEI

ABSTRACT The emphasis of this report is laid mainly on the obtained results regarding tube bulging. This process is relatively new and promising in achieving big deformation of tubular specimens at almost no change in the wall thickness. If the reader would like to know some more of the process itself I also recommend other books and articles, some of them are written in the literature list at the end. In the report I am presenting the results I achieved in the time, I was staying at the Technical University Eindhoven and working with the machine for tube bulging. Some of the tube bulging processes use polyurethane but this one uses oil under pressure up to 400 bar. Steel 35 tubular specimens with outer diameter 60 mm and wall thickness of 2,5 mm were used to test the machine. Tests should have followed a certain model, for we tried to reach a straight strain path.

PREFACE

A Siovenian in the Netherlands? Two professors of mechanical engineering, Prof. Kals from the Netherlands and Prof. Kuzman from Slovenia agreed on exchanging a student each year, that would stay in other country for a period of three months to learn something more about the culture, habits, university, what are they dealing with at the university, and finally to make some research in a specific field. In the year 1995 I was chosen to be an exchange student. I went to the Netherlands for the first time and now, when I am writing my report, I can say I liked being here. People are friendly, especially here at the university. The university has the formal name Technical Universiteit Eindhoven and· is one of three technical universities here in the Netherlands. It has several faculties, one of them, of course, the Mechanical Engineering FaCUlty. The Mechanical Engineering Faculty is divided into three parts: fundamentals, construction and technology and automation. The latter is further divided into subdepartments and Prof. Kals is in charge of Materials and Processing department. That means I was working at this department. There are many researches going on at the time. I was appointed to work with two other students: Ronnie Kanen and Maurice van Beek, both dealing with the problem of hydroforming.


1. LIST OF SYMBOLS

p inside pressure [bar] 0 diameter [mm]

O"a axial stress [N/mm2]

0"., hoop or circumferential stress [N/mm2] E equivalent strain [1 ]

0" equivalent stress [1 ]

0"3 thick.ness stress [1 ]

Do starting diameter [mm] t thick.ness [mm]

to starting thick.ness [mm] C resistance to deformation [N/mm2] n strain hardening coefficient [1 ]

Fa axial force [N]

A area of the end-hole of the tube [mm2]

a. ratio between axial and hoop stress [1 ]

y ratio between axial and hoop strain [1 ]

Fa net axial force [N]

Fseal sealing force [N]

Din inside diameter of the tube [mmJ


1. HYDROFORMING

What exactly is hydroforming? It is a method where a hydrostatic pressure is used alone ore accompanied with other means to act upon a workpiece. Hydrostatic pressure has a nice characteristic; it always acts perpendicular to surface. So an idea is to use hydrostatic pressure in metal forming process together with one more force. If we would be able to reach a state, where during the process two stresses with different sign would act on a workpiece, this would enable us to reach higher deformation, since we would be operating in the second or fourth quadrant of the flow limit ellipse.

1.1 TUBE-BULGING

The process I was working on is called tube-bulging with internal pressure. In the Technical University in Eindhoven there is a machine, that may be used as a test machine for making experiments with tubebulging. As a specimen, a thin-walled cylindrical tube is used. If a tube is thin-walled assumption can be made, that a plane stress state is present. The idea is to fill a tube with oil, seal it, apply axial force on both ends of the tube and simultaneously regulate the pressure of the oil inside the tube. So a condition would be achieved, where a tube would tend to shorten and to expand. It is desired to reach a strain path where the ratio between both major strains, axial and circumferential would be -1. This carries one benefit; the wall thickness remains constant.

1.2 THE GOAL OF THE RESEARCH

The goal of research going on in this field is to determine if it is possible to achieve a constant wall thickness and what is the extent of the deformation, that can be achieved. A model has to be determined that is able to predict forces, strains, stresses at bulge forming processes of workpieces with relatively thin walls would with sufficient accuracy. But to be able to determine something about the process, a proper equipment has to be available. So during my staying here I was dealing with ~he machine, performing some experiments with it to see, what happens. The machine had to be tested since it is just a prototype and never used before. As it is pointed out later, that fact was causing us a lot of trouble. We tried to do experiments according to a model, that would ensure us a straight strain path. We have done several experiments testing the behaviour of both, the machine and the specimen. At the end we have concluded that a better control over the machine is of paramount importance if we want to get some truly valuable results.

I Tadej Campa 4 WPA-TUEI

2. THE SYSTEM

A detailed specification of the machine and system is given at the Ronnie Kanen's diploma thesis. Herewith I would like to point out some negative points which represent an obstacle in thorough investigation of a model that was used for determining strain path, i.e. for determining pressure and axial force at each respective step.

2.1 HOW THE SYSTEM WORKS

At the process pressure and force are controlled by a PC 386-40 computer. The data acquisition card is a PCL-818 card. At the beginning of the process the values for pressure and force, as obtained from the model, are put into a computer. Then the pressure is applied to the machine and a computer program for control over the system is started. That program is written in a Pascal programming language and is a very simple one. As soon as the program is started it sends a first pair of values p-F to the system. Sent value for p determines the amount of pressure inside a specimen and it is achieved very quickly. Sent value for a force is, on the other hand, much slower. This is especially notable when higher pressures together with higher forces are required. When both values are reached (currently there is a 95 % threshold for force implemented in the program) the program sends the next combination of pressure-force. After the program has sent a value it starts to listen to the respond of the system. It reads combinations of values for p-F until both of them are equal to the sent pair and then it sends the next pair of values. This job is repeated until the last pair of p-F values is sent and the corresponding values of the system are received. Both, the sent and received values are written in a file and thus available for further investigation of what was happening at that specific process.

2.2 FLUCTUATIONS OF THE DATA

However, this system is still in a starting phase and as that it is not immune to some child diseases. If the program is tested just with some voltage applied directly to a lab card and that voltage is constant, the data written in a file shows a considerably high amount of fluctuation. This fluctuation increases as the voltage increases, a higher voltage gives higher, fluctuations. In a real process this may cause premature start of a next step or premature stop of a system, as it may happen that due to fluctuations the program gets the required values eventhough in reality they are not yet achieved. What can cause such fluctuations? Undoubtedly there are two possible reasons and most likely both of them are responsible for that. The first reason is hardware. The fluctuations can be generated in any element of the measuring chain. Not only thermal instability itself is to blame for it. There are also other things which we don't know thoroughly.


The second reason is the system itself. It may happen that hydraulic pressure in the system varies in a short period for a significant value due to changes in a position of valves that control an oil flow.

2.3 SUDDEN JUMP

Sudden jump is an instance where one value is constant for longer period of time and then all of a sudden it jumps to a required level causing the program to start with the next step. We don't know yet whether this only represents a true state of that value or there is something wrong with reading the data. In the former case it is the system who is responsible for not implementing the sent values fast enough. In this case it would happen that only after longer time the system would start implementing new values. On the other hand it might really take that much time to achieve those values, but if that was true, then values in a file wouldn't be constant but slowly increasing. If the latter is what's really going on, then there may be something wrong with the frequency of reading the values, maybe the computer reads to slow out of a lab card or a lab card gets values to slow from the process. It can be a sampling frequency responsible for that or the program doesn't read values as fast as it should.

2.4 SERIES OF CONSTANT VALUES

If a file, where pairs of received values for pressure and force are written, is looked upon carefully it may be seen that in most cases the neighbouring values don't differ from one another but are the same and then they change a bit and again remain the same. This goes on through the whole file. What is the cause of this is also not clear. I suppose the system is not to blame for that since it is a real system and that means it is capable of giving an infinite number of different values. What might be responsible for that is again a speed in comparison with a speed of the program. Those two speeds might not be consistent. Or there is some cache memory where the lab card puts its readings and since the program is to slow in reading that data it reads only part of it and after that all the data in the cache memory is replaced with new data event~ough the program didn't manage to read everything. Another responsible factor for this phenomenon might be the sensors. One may say that the sensors may posses a certain threshold when reading data, but they are also real system and therefore they capable of giving quite an amount of different values. But whatever causes this phenomenon is to my mind not as important as the effect of sudden jump which is more crucial for control over the process, since greater values are concerned.


2.5 DISAGREEMENT AMONG SENT DATA AND RECEIVED DATA

As mentioned above the program sends pairs of values for pressure and force to actuators that implement those values. Then the really achieved values are read and sent back to the lab card and to the program. But if someone expects the values are identical or almost identical the one is wrong. The values for force show quite good correspondence with those sent, whereas the values for pressure very much differs from those supposed to be. That is a fact that may significantly influence the whole model and can therefore transform a model being currently used to something completely different. What is responsible for that? The answer seems to be hidden in a lack of feedback loop in this particular system. Therefore if we want to achieve a better control over the process itself a feedback loop with a summation point should be implemented thus giving us the power of better control because the difference between desired and current value would act on a system until the difference would be zero, what would mean the reached value equals the desired one. At the moment there is no feedback loop in the system.

2.6 DIFFERENT SPEED RATE AT CHANGING PRESSURE AND FORCE

When the program sends a pair of values to be reached usually the inside pressure is reached first and the force is always last. The only exceptions may occur due to fluctuations or sudden jump effect. This fact is present because cylinders that generate axial force are bulky thus needing a lot of oil and time to move and to reach the required force, whereas a volume inside a specimen is not that big thus giving the possibility of quicker reactions. In order to reach the required axial force, a lot of oil has to flow to a big axial cylinder what takes a lot more time than the time, necessary to put just a little extra oil to the inside of the tube. This is only one aspect. The other one may be hidden in happenings in the material of the specimen during the process itself. If one take a look at the record with the received values it can see that in some cases it took a lot of time before force reached the desired value. And before this has happened the force varied several times, it varied even downwards. That may point out that something is happening at the material of the specimen. Due ~o a pressure applied the tube is expanding. As the tube is expanding its length is also decreasing therefore both axial cylinders have to get more oil in order to follow the movement of the tube. That is why they can't develop enough force to reach the desired value for force fast enough. Namely, they have to compensate the downward movement of the specimen. Then after some time an equilibrium takes place between the stress caused by the internal pressure and hardening of the material. At that point pressure no longer causes the expansion of the tube and force can now act to a specimen thus establishing the desired ratio alpha, Factor n therewith caused that pressure lost a paramount importance in the process at that moment and axial force took its place. Now the material is forced to flow from both ends of the specimen into


the central and most expanded section providing that way enough thickness to withstand further expansion.

2.7 BURSTING

However a bursting may easily occur as we experienced in our experiments. This may happen out of the following reasons. Firstly, there may be simply to thin wall to withstand the pressure. That may happen because the pressure was to high in comparison with force so the latter couldn't compensate the lost in wall thickness and the tube wall simply fractured. Secondly, a bursting may occur due to end of ductility. That means the maximum extent for deformation had been reached and the material is no longer capable of any further deformation. Because the process still continues, the material fractures at the spot where deformation is highest.

2.8 RESET AFTER EACH SET OF MEASURED VALUES

In order to get appropriate received data it is necessary to reset a computer before starting a new set of observation. This exists due to a fact that computer or a lab card still carries readings of a previous measurement and sends them to a program first. So the program now gets old values from the previous experiment instead of those new ones. This may seriously spoil the measurements, since it can easily happen that at the beginning there are some enormously high values, causing the program to speed up.

3. THE MODEL

The model represents our way in performing experiments. Programmed values for experiments were calculated according to the model. The model we used, was a very simple one, for that was the first model and with it we made our first experiments. We wanted to test the machine and to see what happens at the process therefore we didn't devote to much time to develop a complex model that would take in account all factors. Usually the developing path of the model leads from simple one to those more complex. At developing the model Levy-von Mises' equations were used. Eventhough the geometry throughout the process changes from cylindrical to almost spherical in our calculations we assumed the form of the tube will always be cylindrical. That enables us to use formulas that are valid at axissymetrical states of expansion in order to simplify the calculations of the model. Basic formulas used in determining the model are:

. Campa 8 WPA-TUE

pD 0' =-

<p 2t

eq. 1

eq.2

Both equations, 3 and 4 are better known as Levy-von Mises equations:

E ( as) E<p = 0' O'cp - 2""

eq.3

eq.4

eq.5

Because wall thickness is relatively small regarding to a diameter, equation 6 is valid: 0'3 0

eq.6

eq.7

D 8 =In

<p D o

eq.8

eq. 10

a=C(E +Eor

eq. 11


F;. + pA cra = rrDt

eq.12

If equation 2 is inserted in equation 5 and a small workout is done, a new equation is got:

cr = cr. ~( 1 - a + a 2 )

eq. 13

If equation 1 is put into equations 3 and for and then those two are divided a new factor y, representing the strain ratio is acquired. This factor is called the strain path. It depends on factor a, as the following equation depicts:

Ea 20. -1 Y---- -

E 2-a <p

eq. 14

Out of equations 3,4,10 and 14 we can derive an equation for the wall thickness strain:

E3 = - 28cr crq> [1 + a]

eq.15

If in equation 7 all the 8 values are substituted with their respective natural values and an expression is simplified, a new equation that links equivalent strain with stress ratio and deformation of diameter is made:

_ ~o.2-a+l 8 = 28. 2 -a

eq. 16

Further on if equations 1 and 13 are coupled it can be seen that: an pD

cr - --<p- ~a2 -0.+1 - 2t

eq. 17

The wall thickness can be expressed with help of equations 9, 15 and 16 as follows:

D In - (1 +a)

Do t = to exp(E3) = to exp(- )

2-a

eq.18

Finally, the axial force, that has to be applied to a specimen equals:


eq. 19

Fe is a part of equation that holds a balance with the circumferential stress, whereas FseaJ is a sealing force, that prevents oil from leaking. F& = Ct.cr.,rr.Dt

eq.20

FHal = - pA=-

eq.21

Din equals 55 mm in our experiment. This is a diameter at both, upper and lower end, where a die of the machine is in contact with the specimen thus providing sealing and axial force.

All those equations were put into an Excel spreadsheet where the values for p and F were obtained for each value of D at specific Ct..

3.1 DIFFERENT RESULTS AS EXPECTED

Model represented above is an ideal one and we tried to use it. However in reality, pressure given by the machine is always higher than programmed. So, eventhough the values for pressure didn't correspond to those the model predicted, we got good results and quite good expansions. Why? First of all, in the model for all experiments we made one mistake, that later proved as a counterbalance for that surplus of the system's pressure. Namely, instead of taking Din for the diameter, where sealing is necessary, the largest diameter at that moment was taken into account. So, the sealing force was increasing exponentially and was dependent on both variables, p and D, eventhough according to the above model it should depend only upon pressure p. But as I mentioned earlier, this in fact helped us to get good results. In reality the pressure differed from the programmed pressure exponentially also. That meant a higher sealing force and also a higher axial force were necessary. Both of those requirements were successfully compensated by the mistake we made by taking D instead of Din into equation 21. To make this story clearer let me tell you that in our experiments usually just values that permitted the extension up to 65,5 mm were programmed. Well, in all the instances the highest diameter was well above that figure. In one case it was as high as 91,5 mm!

3.2 CORRECTING THE SEALING FORCE

The sealing force has to be recalculated and the model has to be changed in the way that for calculating the sealing force the Djn is used. That reduces the sealing force necessary. This would recalculation shows, that a greater share of the acting axial force is used to participate in holding


the ratio a. higher. Experiments 14 and 15 have taken this in account while calculating the real a..

3.3 DESCRIPTION OF THE SPECIMENS

For making tests specimens with the following geometry were used:

outer diameter: inside diameter: wall thickness: length:

Material used is:

60mm 55 mm 2,5 mm 130 mm

material mark: St35 Werkstoffnummer: 1.0308 DIN 1629 BL.3 ISO DIS 2604 T2

Chemical composition:

element

C Si Mn P S N

percent

<=0,18% < =0,35% > =0,40% < =0,050% < =0,050% < =0,007%

Important! At first experiments specimens were not annealed so there was an undetermined rate of predeformation present. Therefore it was not possible to get exact data on mechanical properties. However, in later experiments annealing has been carried out at 6900

• for one hour with subsequent cooling in the furnace to room temperature. In that case it was possible to determine material properties:

Rm = 350 to 450 N/mm2 E = 210000 N/mm2 RpO•2 = 240 N/mm2 strain at failure = 25 %

3.4 RESULTS

In this paragraph a short description of achieved results is presented. Number of the results shows also the number of the file, where data is recorded. All test with endings MOD or EXP were carried out with annealed specimens.


4.exp a =-0,2 dmax =80,5 mm I = 116 mm deformed

5.exp a =-0,2 dmax =81,5 mm I = 115,5 mm deformed

6.exp a =-0,1 dmax = 88,0 mm I =114 mm deformed and bursted

7.exp a =-0,15 dmax =78,5 mm I =117 mm deformed

8.exp a =-0,2 taken by representatives of the firm that contributed money deformed

9.exp a =-0,2 dmax =91,5mm I =110 mm deformed

10.exp a . =-0,2 dmax =92 mm I =109 mm deformed

11.exp a =-0,2 taken by Mr. Ronnie Kanen deformed


12.exp a =-0,15 dmax =92 mm I =110 mm deformed and bursted

14.exp a =-0,2 dmax =88 mm I =112 mm

15.exp a =-0,2 dmax =89 mm I = 112 mm

NOTE: In all those cases a is given as it is supposed to be according to the model.

3.5 DETERMINING REAL a

Those experiments were all carried out according to a model, that used a constant value for a. But note, that that value is not constant during the experiment! For determining the real a, that is valid during the test, an on-line measurement of the diameter is necessary. In experiments 14 and 15 we have done measurements of the diameter according to time. Time is related to force and pressure applied on a specimen. If the program reads values at intervals of 500 ms, it should be possible to chart a diameter vs. force-pressure relationship. We used a diameter gauge fixed to the machine that measured diameter. After the pressure was applied to the system, readings were written down every 5 seconds. Then readings were compared with the force and pressure received at that time interval. So a certain relationship was established. The results for a, calculated out the measurements using iteration, were surprisingly low. They are near O! That implies, that axial force should be significantly increased. But here we are limited with another boundary -the buckling limit.

3.6 EXACTNESS OF REAL a

The method used was very primitive one. The tip diameter gauge was pointed at the centre of the specimen in order to measure the deformation at a place where the deformation rate is highest. But since only the upper die is moving and the lower is almost standing still, the tip of the gauge is not measuring the change of the diameter in the same point. That is one contribution to uncertainty of the acquired diameter change.


fig.1

Other thing is the way of making readings. How reliable is a reading made from a distance and with a certain angle? There is namely a plexi plate between a reader and a diameter gauge. Also the readings cannot be made exactly at the time period of 5 seconds. Last, but not least, there is a computer program. It is true that it is programmed to read values at every half a second. But what is that time interval in reality? And are those read values correct? I mentioned earlier, that also the received values, computer gets, are not completely certain. Because of importance of assigning each measured diameter to appropriate pressure and force, those measurement, we got, could be tricky. Nevertheless, we used them just to get a feeling of what is happening at the process. To improve accuracy, an on-line measurement with strain gauges should be implemented. In that case, a computer could be used to record readings from a strain gauge. Strain gauges should be fixed around a perimeter in different directions and tied up in Wheatstone's bridges.

3.7 WALL THICKNESS

The majority of the experiments were carried out under the same settings, that is values for force and pressure were programmed according to the model where a was -0,2. My comment will assume that settings unless stated different. The results show the extent of the deformation, that is achieved at the programmed value for a. It can be seen that the largest natural strain is as high as E=0,42. The form of a deformed tube tends to be eliptoidical, almost spherical. In one case the with the usual programmed values for a = -0,2 the deformed specimen was cut and a wall thickness has been measured. The average wall thickness at the most expanded rim is 1,9mm. Then it slowly increases to the end where it is as high as 2, 47 mm (that means no change here regarding to the starting diameter).


In experiment 11 a bursting occurred eventhough the settings were according to model a=-0,2. That shows the process is not stable and the control over the system parameters is poor. Plastic deformation is limited by: • necking which is a phenomenom due to an instability condition in

tension when uniform plastic flow ceases and becomes localised resulting in local thinning of the workpiece

• buckling which is associated with a transition phenomenon between elastic and plastic stress states • fracture which is a separation process Those are the reasons that in certain cases an experiment ends in a non desired way-with one of the above characteristics.

4. THE CONCLUSION

In this process a relationship of ex. = -1,0 is pursued. That means that 0'."

equals 0'9 and also 6", is equal to 6",. hence thickness strain 63 = O. By that way we assure that wall thickness stays constant. Because of thin walls an assumption is made that 0'3 = O. According to the Keeler-Goodwin diagram, in the case of ex. = -1,0, large equivalent strains could be achieved before material fractures. But this depends also on a rate of predeformation. That is why we mostly used annealed tubes to get rid of all the effects that predeformation causes. The machine itself was constantly causing difficulties. It took a lot of time and preparation to carry out an experiment. Also the number of tubes was limited and because some demonstration were held, it wasn't possible to do more experiments with different ex. to see, what happens. That's why I had to work with the data I have obtained. I think it is necessary to do the following changes and improvements on the machine: • feedback loops must be implemented in order to achieve accurate

parameter values and a good response of the system • on-line measurement of the diameter must be implemented, preferably by strain gauges so that a computer can store electric signals they send and process it; the other possibility is with a normal diameter gauge, just as we did at the end. At that case a person has to read values during the operation of the machine. • number of cables must be rationalised in order to prevent misconnection and the possibility of a bad contact • movement of the upper and lower plunger must be measured in order to know the displacement • the program has to display all the parameters on screen With the current state of the equipment, no reliable results can be obtained. So the machine needs improvements!


But is it possible to achieve a strain path, where a = -1,0 in a free bulge forming process? It is necessary to perform more experiments with higher a just to see what happens. As far as we know, even at much lower ratio for a a specimen buckles. We did only one experiment where ratio a was -0,4 instead of -0,2. In that case buckling occurred. But to my view, one experiment is not enough to say with reasonable sureness what would happen at that ratio. So in the future the limits of the process are still interesting field for research. Also finite element method may be used here to see, how the material acts under strains present in the process. This method would also give more precise answers to what is happening with the specimen in the respective phases, while it is undergoing the process. The research, done here in Eindhoven, is dealing with tube-bulging in the open die. This enables us to actually see, what is going on during the process. The other possibility is using a closed die, where expansion can be much bigger, but then monitoring of the process is not possible. And someone has to study how the tube reacts, when there is no constraints, in order to get better knowledge of the process. Despite the difficulties, I can say that we managed to reach the deformations as big as 50 %. The pressure inside the tube reached a value of 325 bar at axial force 105000 N and programmed a was -0,2. The tubes, that were deformed most, posses a maximum diameter of 92mm. This is very close to the upper limit of expansion without an interstage annealing. The process of tube-bulging is not very old. Regardless, some automobile factories use it in production of differential casings. However, they use closed die geometry. Products, made by this process can be used further in automobile industry. Production of cam shafts is a possible field, where it might be implemented. The cam shafts could be hollow. If this would be the case, then tube-bulging is a good process to do it. However, it has to be checked, if the hollow cam shaft can stand all the stresses and loads.

5. ACKNOWLEDGEMENT

I would like to thank all the students and personnel here at the university, for all. the help, support and encouragement they were offering to me. Also my thanks to both professors; Prof. Kals and Prof. Kuzman for making the decision of exchanging students. I wish success to everyone in his field of research or study.


6. LITERATURE LIST

[1] Franc Gologranc: Preoblikovanje 1.del, Fakulteta za strojnistvo, Ljubljana 1991 [2] W.J. Sauer, A. Gotera, F. Robb, P. Huang: Free Bulge Forming Under Internal Pressure and Axial Compression, Carnegie-Mellon University, Pittsburgh, PA, p.228-235 [3] D.M. Woo, P.J. Hawkes: Determination of Stress/Strain Characteristics of Tubular Materials, Journal of Institute of Metals, Vo1.96, p.357-359, 1968 [4] Alfons Boehm: Numerische Simulation von Verfahren der Innehochdruckumforming unter besonderer Beruecksichtigung des Aufweitens im geschlossenen Werkzeug

ITadej Campa 18 WPA-TUEJ

Technische Universiteit Eindhoven Faculteit Werktuigbouwkunde Vakgroep Produktietechnologie en Automatisering


Appendix

Tadej Campa

April 1995 WPA 120031

1. APPENDIX 1.1 THE MODEL 1.2 PROGRAMMING THE VALUES 1.3 EXPERIMENT 15 1.4EXPERIMENTI4C 1.5 EXPERIMENT 12 1.6 EXPERIMENTS 11 AND 10 1.7 EXPERIMENTS 9 AND 8 1.8 EXPERIMENT 6

2. DIAGRAMS AND TABLES

ii ii ii iii iii iv iv iv iv

1

1. APPENDIX

Here are presented some of the experiments accompanied with values and diagrams. Also the model is presented according to which pressure and force were used in controlling the process and a recommended set of values that should enable to perform a successful demonstration.

1.1 THE MODEL

In this model the ratio between an axial stress and circumferential stress was 0.=-0,2. According to that ratio and material properties, other values were calculated, A ratio 0.=-0,2 was a common setting during our experiments, because in most cases this ratio assured us the nice result will occur. The model is presented on pages 1 and 2. Most of the experiments were carried out at programmed ratio of 0.=-0,2. At calculating the model, I was using basic equations, as shown at the report.

1.2 PROGRAMMING THE VALUES

When doing an experiment, first a certain a had to be chosen. Then values, as the model returned for that particular a, are put into the computer. However in programming pressure and force we used only first 11 values from the model. Then some pairs of values were programmed, where values for pressure and force were decreasing just to assure, the oil will not leak out of the plunger. That is why a common table with programmed values includes also decreasing values what makes 15 steps. A table which was the most used, is given below. It will in most cases guarantee nice demonstartions, where deformations of around 50 % are reached.

ii

step force [N] pressure [bar]

1 I 50000 0 2 54600 136 3 66200 162 4 74100 178 5 80400 190 6 85800 200 7 90500 207 8 94700 213 9 98600 218 10 102100 223 11 105500 227 12 108600 230 13 74100 178 14 54600 136 15 50000 0

fig.1

1.3 EXPERIMENT 15

This experiment was performed according to the model. However, what was really happening, is not very close to the model. This model is special because a primitive on-line diameter measurements were made with a diameter gauge, mounted inside the working space of the machine. That enabled us to know what is the diameter at a certain combination of force and pressure, and thus we were able to calculate all the necessary parameters for determining the real ex. during the process. On pages from 3 to 9, a set of values is given, where it can be seen, what were the real pressure and force at the system. The page 12 clearly depicts, that real ex. is very close to zero. A sudden increase in the value ex. at the end is present due to a way the system ends the process and can be disregarded. The proof for inaccuracy of the system is clearly visible on a page 10 where both pressures, the desired one and the real one, are compared. The way the system makes changes in the values for pressure and axial force is presented on a page 11. The x-axis can also represent time.

1.4 EXPERIMENT 14C

This experiment was also performed with an on-line diameter measurement. All the data, containing the readings from the system and on-line diameter measurements with some values, calculated afterwards,

iii

is shown on pages 13 to 16. The real ratio between axial and circumferential stress that was calculated also here gives the result close to zero, as the graph on page 19 shows. Page 17 shows the surplus of the real pressure in the system and page 18 shows, how the parameters of the system, pressure and force, are distributed according to steps (time).

1.5 EXPERIMENT 12

Thi experiment was one of the few, where the ratio ex. was a bit lower. In this experiment ex. was -0,15. However, at this ex. the specimen underwent a failure. A crack appeared on the surface, causing an explosion. The form of the crack may show that this fracture occurred due to the end of ductility. At this experiment and all the rest with the lower number mentioned in this appendix, no on-line measurement of the diameter of the expanding tube were made, so no data representing pressure and force in table form is given. It is presented only in schematic way. Page 20 shows, the programmed values and the values reached. It can be seen, that the pressure when burting occurred, was 323 bar. A mark N points out that the step 11 was never reached, since the fracture took place earlier.

1.6 EXPERIMENTS 11 AND 10

Those two experiment both gave nice results. Both experiments, as well as all the previously described (except the one, that bursted). reached all the programmed values and ended because all the values in the computer program were reached. The parameters of the processes are shown in appropriate charts.

1.7 EXPERIMENTS 9 AND 8

The two experiments, described here, were similar to all the above described ones, just that here, the process was prematurely stopped. At this phase we still didn't allow the process the time, necessary to reach the en,d of the program, but we interrupted it.

1.8 EXPERIMENT 6

The parameters of this experiment are presented on pages 30 and 31. This one also ruptured. The form of the crack, that appeared, shows the possibility, that in this case the wall thickness wasn't able to stand the inside pressure.

iv

MODEL

DEFINED VALUES alpha

~0,2

C diameter eps fi eps equiv sigma fi p [bar) Fseal[N) Faxi [N) sigma_the Cthicknes F theta Faxi [N] 667 60 0 0 0 0 0 0 0 2,50000 0 0

n 60,5 0,00830 0,00840 164,8106 135,7967 ~39038 ~54653 ~32,9621 2,49247 ~15615 ~54653

0,27 61 0,01653 0,01673 198,5087 161,737 ~47267 ~66174 ~39,7017 2,48502 -18907 ~66174

Do [mmJ to [mm] 61,S 0,02469 0,02500 221,23 178,254 ~52952 ~74132 -44,246 2,47765 ~21181 -74132 60 2,5 62 0,03279 0,03319 238,8364 190,327 ~57461 ~80445 ~47,7673 2,47037 -22984 ~80445

AUXILARY VALUES 62,S 0,04082 0,04132 253,3917 199,7264 -61275 -85785 -50,6783 2,46316 -24510 -85785 sq. root 63 0,04879 0,04939 265,8891 207,3122 ~64624 ~ 5604 -25850 -90474

1,01232 63,5 0,05670 0,05739 276,8909 213,5755 -67638 899 -27055 -94693 64 0,06454 0,06533 286,7491 218,8264 -70396 01 -28159 -98555

64,5 0,07232 0,07321 295,7003 223,2753 -72954 11 -29182 -102136 65 0,08004 0,08103 303,9119 227,072 -75349 828 -30140 -105489

65,5 0,08771 0,08879 311,5073 230,3276 -77610 -1 - , 15 153 -31044 -108654 66 0,09531 0,09648 318,58 233,1271 -79757 -111660 -63,716 2,41484 -31903 -111660

66,5 0,10286 0,10412 325,2029 235,537 -81807 -114530 -65,0406 2,40822 -32723 -114530 67 0,11035 0,11171 331,4342 237,6106 -83773 -117283 -66,2868 2,40167 -33509 ~117283

67,5 0,11778 0,11923 337,3209 239,3914 -85666 -119932 -67,4642 2,39519 -34266 -119932 68 0,12516 0,12671 342,9016 240,9152 -87493 -122490 -68,5803 2,38877 -34997 ~122490

68,5 0,13249 0,13412 348,2087 242,212 -89262 -124967 -69,6417 2,38241 -35705 -124967 69 0,13976 0,14148 353,2693 243,3072 -90979 -127371 -70,6539 2,37612 -36392 -127371

69,S 0,14698 0,14879 358,1066 244,2223 -92650 -129710 -71,6213 2,36989 -37060 -129710 70 0,15415 0,15605 362,7406 244,9762 -94278 -131989 -72,5481 2,36372 -37711 -131989

70,S 0,16127 0,16326 367,1885 245,5849 -95867 -134214 -73,4 -38347 -134214 71 0,16834 0,17041 371,4653 246,0625 -97421 -136389 -74,2 -38968 -136389

71,5 0,17535 0,17751 375,5843 246,4216 -98942 -138519 -75,1 -39577 -138519

72 0,18232 ~~ -100433 - -40173 -140606 72,5 0,18924 0, -101896 - -40758 -142654

73 0,19611 0,19853 387, 246,8905 -103333 -144667 -77,421 2,32792 -41333 -144667 ~ 0,20544 390,6 2 -104746 -146645 -78,1395 2,32215 -41898 -146645

74 0,20972 0,21230 394,1794 246,7812 -106137 -148591 -78,8359 2,31643 -42455 -148591

1

MODEL

74,5 0,21645 0,21912 397,5575 246,621 -107506 -150508 -79,5115 2,31077 ·43002 -150508 75 0,22314 0,22589 400,8378 246,3981 -108855 -152398 -80.1676 2,30515 -43542 -152398

75,5 0,22979 0,23262 404,026 246,1178 -110186 -154261 -80,8052 2,29959 -44074 -154261 76 0,23639 0,23930 407,1272 245,7847 -1~ 2,29408 -44600 -156099

76,5 0,24295 0,24594 410,1461 245,403 -11 2,28861 -45118 -157914 77 0,24946 0,25253 413,087 244,9766 ·114076 -1 , 2,28320 -45631 -159707

77,5 0,25593 0,25909 415,9539 244,5092 -115342 -161479 -83,1908 2,27783 -46137 -161479 78 0,26236 0,26560 418,7503 244,0038 -116 -83,7501 2,27251 -46638 -163231

78,S 0,26875 0,27207 421,4798 243,4636 -117 -84,296 2,26724 -47133 -164965 79 0,27510 0,27849 424,1454 242,8913 -11 -84,8291 2,26201 -47623 -166680

0,28141 0,28488 426,7501 242,2894 -12027 5,35 2,25682 -48108 -168378 80 0,28768 0,29123 429,2965 241,6602 -121472 5169 -48589 -170060

80,5 0,29391 0,29753 431,7873 241,0059 -122662 4659 -49065 -171727 81 0,30010 0,30380 434,2247 240,3286 -123841 4154 -49536 -173378

81,S 0,30626 0,31003 436,611 239,63 -125010 -175015 -87,3222 2,23653 -50004 -175015 82 0,31237 0,31622 438,9483 238,9118 -126170 -176638 -87,7897 2,23156 -50468 -176638

82,S 0,31845 0,32238 441,2385 238,1758 -127320 -178247 -88,2477 2,22663 -50928 -178247 83 0,32450 0,32849 443,4835 237,4232 -128460 -179845 -88,6967 2,22174 -51384 -179845

I 83,S 0,33050 0,33457 445,6849 236,6556 -129592 -181429 -89,137 2,21690 -51837 -181429 84 0,33647 0,34062 447,8444 235,8742 -130716 -183002 -89,5689 2,21209 -52286 -183002

84,S 0,34241 0,34663 449,9636 235,0802 -131832 -184564 -89,9927 2,20732 -52733 -184564 85 0,34831 0,35260 452,0439 234,2746 -132939 -186115 -90,4088 2,20259 -53176 -186115

u5,5 0,35417 0,35854 454,0866 233,4586 -134039 -187655 -90,8173 2,19790 -53616 -187655 86 0,36000 0,36444 456,0931 232,6331 -135132 -189185 -91,2186 2,19324 -54053 -189185

86,5 0,36580 0,37031 458,0645 231,799 -136218 -190705 -91,6129 2,18862 -54487 -190705 87 0,37156 0,37614 460,0021 230,9571 -137297 -192215 -92,0004 2,18404 -54919 -192215

87,5 0,37729 0,38194 461,907 230,1083 -138369 -193716 -92,3814 2,17949 -55348 -193716 88 0,38299 0,38771 463,7802 229,2532 -139435 -195208 -92,756 2,17498 -55774 -195208

88,5 0,38866 0,39345 465,6227 228,3926 -140494 -196692 -93,1245 2,17051 -56198 -196692 89 0,39429 0,39915 467,4355 227,5271 -141548 -198167 -93,4871 2,16606 -56619 -198167

89,5 0,39989 0,40482 469,2195 226,6573 -142595 -199634 -93,8439 2,16166 -57038 -199634 90 0,40547 0,41046 470,9755 225,7837 -143637 -201092 -94,1951 2,15728 -57455 -201092

90,5 0,41101 0,41607 472,7045 224,907 -144674 -202543 -94,5409 2,15294 -57870 -202543 91 0,41651 0,42165 474,4071 224,0276 -145705 -203987 -94,8814 2,14863 -58282 -203987

91,5 0,42199 0,42719 476,0841 223,146 -146731 ·205423 -95,2168 2,14435 -58692 -205423 92 0,42744 0,43271 477,7364 222,2625 -147751 -206852 -95,5473 2,14011 -59101 -206852

2

experiment 15

p [bar] F [N] t[s] O[mm eps_fi Fseal[N] Ftheta [N] Cmod [mm sigma_th sigma fi alpha 2,5 0

17 0 17 0,5 44 43729

110 43729 162 43729 165 437 167 169 169 43729 169 169 5 60 0 40152 -3578 2,5 -7,59193 1267,5 -0,00599 169 43729 5,5 168 43729 6 168 43729 6,5 168 43729 7 168 43729 7,5 168 43729 8 169 56388 8,5 169 56388 9 211 56388 9,5 211 61374 10 60 0 50243 -11131 2,5 -23,6203 1586,08 -0,01489 212 61374 11 212 61374 11 212 61374t::lli 213 61374 213 61374 212 61374 13 212 61374 14 21"1 61374 14 40 61374 5

209 61374 60,2 0,003328 49663 -11711 2,4959414 -24,8092 1570,44 -0,0158 209 61374 16 209 61758 16 208 61758 17 208 61758 17 208 61758 18 208 61758 18

617 9 ~ 208 59840 20 61 0,016529 49315 -10525 2,4798541 -22,1465 1569,97 -0,01411 208 59840 21 208 59840 21 208 59840 22 208 59840 208 59840 208 59840 208 59840 208 208 209 25 61,6 0,026317 49605 -12536 2,4681177 -26,2463 1587,19 -0,01654 209 62141 26 209 62141 26

3

experiment 15

210 62141 27 210 62141 27 210 62141 28 210 62141 28 210 62141 29

11 6214'1 29 12 66744 30 12 66744 3 62 0,03279 359 -16385 2,4606127 -34,187 1616,85 -0,02

237 66744 31 237 66744 31 237 66744 32 237 66744 32 237 67895 33

7 67895 33 7 67895 34

237 67895 34 47 67895 35

237 67895 35 62,4 0,039221 56335 -11560 2,4524013 -24,0452 1814,31 -0,01325 237 67895 36 237 75183 36 238 75183 37 257 75183 37 257 75183 38 258 75183 38 258 75183 39 258 73649 39 258 73649 40 258 73649 40 63 0,04879 61267 -12382 2,4408971 -25,6306 1982,76 -0,01293 258 73649 41 258 73649

* 258 73649 58 73649 58 73649 43

258 73649 43 258 73649 44 258 73649 44 259 73649 45 259 73649 -W 63,4 0,055119 61499 -12150 2,4332964 -25,0697 1996,67 -0,01256 259 81321 259 81321 46 273 81321 47 273 81321 47 273 81321, 48 273 80554 48 273 80554 49 274 80554 49 53 80554 50

274 80554 50 64 0,064539 65038 -15516 2,4223611 -31,8568 """","'''''' -0,01501 274 80554 51 274 80554 51 274 84773 52

Hi 84773 52 84773 53 84773 53

286 84773 54

4

experiment 15

285 83622 54 285 83622 55 285 85540 55 64,6 0,07387 67823 -17717 2,4115038 -36,2019 2223,57 -0,01628 286 85540 56 286 85540 56 286 85540 57 286 85540 57 286 85540 58 286 85540 58 286 85540 59 286 85540 59 287 85540 60 287 85540 60 65,2 0,083115 68113 -17427 2,4005798 -35,4421 2243,61 -0,0158 287 85540 61 m«O 61

91678 62 91678 62

57 91678 63 305 91678 63 304 91678 64 304 91678 64 56 91678 65

304 91678 65 66,2 0,098336 72116 -19562 2,3 -39,4717 2394,17 -0,01649 303 91678 66 304 89760 66 304 89760 67 303 89760 67 304 89760 68 304 89760 68

~60 69 60 69

303 89760 70 304 89760 70 67 0,110348 72116 -17644 2,3686586 -35,3884 2408,6 -0,01469 304 93979 71 304 93979 71 314 93979 72 ~979 72 313 93979 73 313 93979 73 313 92061 74 313 92061 74 59 92061 75

9206t 75 68,4 0,131028 7 7741 2,3446741 -35,2109 2508,44~ 3131 92061 76 313 61 76 313 92061 77 313 9206'1 77 313 92061 78 313 92061 78 313 95130 79 313 95130 79

~30 80 130 80 69,4 0,145542 74321 ·20809 2,3286189 ·40,9672 2527,69 -0,01622

313 96281 81 313 9628'1 81

5

experiment 15

313 96281 82 313 9628'1 82 313 96281 83 313 96281 83 313 96281 84 313 96281 84 313 9628'1 851 313 96281 851 70,4 0,159849 4263 -22018 2,312612 -4 01692 313 97815 86

313 9781~fI 320 97815 320 97815 87 ~815 88

3 94746 88 320 94746 89 320 94746 89 320 94746 90 320 94746 90 72 n1 76061 -18685 2,2864307 -36,1289 2635,17 -0,01371 320 94746 91 320 94746 91 320 94746 92 320 94746 92 320 94746 93 320 94746 93 320 94746 94 320 95897 94 320 95897 95 320 95897 95 0,201579 76003 26517231 -38,0866 2659,41 ·0,01432 320 95897 96 320 95897 96 320 95897 97 320 958971 97 320 95897 98 320 95897 98 320 96664 99 320 96664 99 320 96664 100 320 96664 100 74.8 0,220473 76003 ·20661 2,2444238 -39.1738 2685,31 -0,01459 320 96664 101 320 96664 101 320 96664 102 320 96664 102 320 96664 103 320 96664 103 320 96664 104 320 97048 104 320 97048 105 320 97048 105 76.2 0,239017 76061 -20987 2,2241349 -39,4164 2712,91 -0,01453 320 97048 106 320 97048 106 320 97048 107 320 97048 107 320 97048 108 320 97048 108 320 97048 109

6

experiment 15

62 97048 109 320 96664 110 320 96664 77,4 0,254642 76003 -20661 2,2070169 -38,4996 2732,34 -0,01409 320 96664 320 96664 320 96664 320 96664 320 96664 320 320 320 320 97048 320 97048 I 79 0,275103 75945 - -38,9138 2758, 320 97048 116 320 97048 116 320 97048 117 320 97048 117 320 97048 118 320 97048 118 320tij 320 9704 320 9704 320 80,4 0,29267 76003 -21045 2,1661813 -38,4628 2785,72 -320 97048 121 320 97048 121 320 97048 122 320 97048 122 320 97048 123 320 97048 123 320 97048 124 62 97048 124

320 97048 125 320 97432 125 81,8 0,309933 76 2,1479486 -38,8203 2810,38 -0,01381 320 97432 126 320 97432 126 320 9740 320 9743 320 97432 128 320 97432 128 320 97432 129 63 97432 129

320 97432 130 320 97432 130 83 0,324496 75945 -21486 2,1326046 -38,6387 2829,07 -0,01366 320 97432 131 320 974 320 320 97432 320 97432 319 97432 320 319 319 135 319 99350 135 84,4 0,341223 75887 -23462 2,1157409 -41,8229 2851,86 301467 319 99350 136 319 99350 136

7

experiment 15

319 99733 137 319 99733 137 320 99733 138 319 99733 138 320 99733 139 319 99733 139 319 99733 140 319 99733 m 85,6 0,355341 -23904 2,1012226 -42,303 2870,37 -0,01474 319 99733 319 99733 141 319 99733 142 319 101267 142 319 101267 143 326 101267 143 325 101267 144 =m1267 144

1267 145 325 101267 145 87 0,371564 77280 -23988 2,0843548 -42,1064 2949,25 -0,01428 325 101267 146 325 101267 146 325 101267 147 325 101267 147 325 10126~H*t 325 102035 325 102035 149 325 102035 149 325 102035 150 325 102035 150 88 0,382992 77222 -24813 2,0729224 -43,2975 ,56 -0,01461 326 102035 151

~O35 151 102035 152

5 103569 152 325 103569 153 280 103569 153 280 103569 154

~103569 154 103569 155 103569 ~88,4 0,387527 66198 -37371 2,0746914 -64,8597 2555,1 -0,02538 103569 15

278 103569 156 278 103569 157 278 88609 157 278 88609. 158 278 88609 158

~88609 159 88609 159

277 88609 160 200 88609 160 88,4 0,387527 47459 -41150 2,082483 -71,1526 1838,67 -0,0387 187 50634 161 187 50634 161 187 50634 162 187 50634 162 187 50634 163 188 50634 163 188 50634 164

8

experiment 15

40 50634 164 188 50634 165 ltsts 50634 165 89 0,394292 44558 -6076 2,0564066 -10,5675 1716,23 -0,00616 188 50634 166 188 50634 166 187 50634 167 143 50634 167 105 60991 168

81 60991 168 67 60991 169 53 60991 169 52 60991 170 89 0,394292 12242 -48749 2,1472726 -81,1965 492,352 -0,164921

9

experiment 15

programmed values p [bar] F [N] reached values preal [bar] Freal [N] step 'I 0 50000 step 1 17

2 135 54654 2 169 56388 3 161 66173 3 212 66744 4 178 74132 4 237 75183 5 190 80445 5 259 81321

~ ____ ~ _____ 6~ ___ 199 ~8~57~8~5+-____ ~ ____ ~6~ __ ~ 7 90474 7

84773 91678

8 94692 8 91678 9 98554 9 93979

10 102136 10 97815 11 105589 11 101267 12 108654 12 103569 13 190 80445 13 88609 14 135 54653 14 60991 15 50 50000 15 60991

programmed vs. real pressure in exp.15

350

300

250

200 'i:' -+-p[bar] ! CI. -III-preal [bar]

150

100

50

0 0 2 4 6 8 10 12 14 16

step

10

experiment 15

pressure and force vs. steps in expo 15

350 120000

300 100000

250 80000

200 'i:' -III

60000 ~ :e. A- LI.

150

40000 100

50 20000

0 0 1 27 53 79105131157183209235261287313339365391417443469

step

11

experiment 15

alpha and diameter during the process 15.exp

90 o

·0,02

85

-0,04

80 -0,06

... -0,08 S as e 75

.J::. Q.

as iii :s ·0,1

70 -0,12

__ 0 [mm]

-0,14 • alpha

65

-0,16

60 -0,18

0 20 40 60 80 100 120 140 160 180 time [s]

12

experiment 14C

P [bar) F [N] 1[s] O[mm eps fi Fseal[N] Ftheta [N] t mod [mm sigma th sigma fi alpha 2,5 0

17 56771 0 65 0,08",,,,.,,, '. 'i7 -"II .. V"" 2,4813355 -103,912 139,821 -0,74318

29 56771 0,5 44 56771 1

111 56771 1,5 163 56771 2 33 56771

~ 5677 5677 5677 56771 56771 65 0,080043 50243 -6528 2,4030793 -13,3024 1651,64 -0,00805

212 56771 5,5 212 66744 6 212 66744 6,5 241 66744 7 241 66744 7,5 241 66744 8 241 66744 8,5 241 66744 9 241 66744 9,5 242 66744 10 65 0,080043 57380 -9365 2,4033739 -19,0816 1886,46 -0,01012 241 75567 11

48 75567 11 260 75567 12

75567 12 75567 13 83239 13 83239 14

54 83239 14 89 83239 15

289 83239 15 65 0,080043 68577 -14662 2,4038204 -29,8689 2255,01 -0,01325 288 83239 16 288 83239 16 288 83239 17 288 83239 17 288 90527 18 288 90527 18

58 90527 19 305 90527 19 304 90527 20 304 90527 20 65,8 0,092275 72116 -18411 2,3898376 -37,2674 2386,61 -0,01562 304 90527 21 304 90527 21 303 90527 22 04 90527 22 03 90527 23

304 90527 23 ~ 90527 24

30 90527 24 303 90527 25 303 90527 25 66,8 0,107359 72058 -18469 2,3722644 -37,098 2403,13 -0,01544 60 90527 26

304 90527 26

13

experiment 14C

304 90527 27 303 95130 27 304 95130 28 314 95130 28 313 95130 29 313 92061 29 313 92061 30 313 92061 30 67,6 0,119263 74321 ·17741 2,3582522 ·35,4225 2493,46 ·0,01421 313 92061 31 313 92061 31 313 93979 32 313 93979 32 313 93979 33 313 93979 33 313 93979 34 313 93979 34 313 95514 35 313 95514 35 69 0,139762 74321 ·21193 2,3352912 -41,8647 2520,32 -0,01661 i 313 95514 36 313 95514 36 313 95514 37 313 95514 37 313 95514 38 313 95514 38

~95514 39 313 95514 39 313 95514 40 313 95514 40 69,6 0,14842 74379 -21135 2,3254003 -41,5663 2533,44 -0,01641 313 98199 41 63 98199 41

321 i 98199 42 321 98199 42 321 98199 43 321 98199 43 320 98199 44 320 95897 44 320 95897 45 320 95897 45 71,2 0,171148 76061 -19836 2,2992707 -38,5683 2620,53 ·0,01472 62 95897 46

320 95897 46 320 95897 47 320 95897 47 320 97048 48 321 97048 48 320 97048 49 321 97048 49 32'1 97048 50 320 97048 50 72,8 0,193371 76119 -20929 2,2745632 -40,231 2652,65 ·0,01517 320 97048 51 320 97048 51 320 97048 52 320 97048 52 320 97048 53 320 97048 53 32'1 97048 54

14

experiment 14C

320 97815 54 320 97815 55 321 97815 55 74 0,209721 76177 -21638 2,2565461 -41,2465 2677,05 -0,01541 321 97815 56 320 97815 56 62 97815 57

320 97815 57 321 97815 58 320 97815 58 321 97815 59 320 97815 59 320 98199 60 !

320 98199 60 75,6 0,231112 76027 -22172 2,2331137 -41,80481 2701,17 -0,01548 32~~ 61 I

320 98199 61 320 98199 62 321 98199 62 !

321 98199 I 63 320 98199 63

32~~99 64 320 199 64 321 98199 65 320 9819~H 77,2 0,252055 76027 -22172 2,2102503 -41,3619 2730,1 -0,01515 321 98199 321 98199 66 321 97815 67 320 97815 67 320 9:~B 320 97 8 320 97815 9 320 97815 69 320 97815 70 320 97815 70 78,8 0,272568 761 -21696 2,1879171 -40,056'1 2761,89 -0,0145 320 97815 71 320 97815 71 320 97815 72 320 97815 72 321 97815 73 320 97815 73 320 97815 =w 320 97815 320 97815 75 320 97815 75 80 0,287682 76027 -21789 2,1717342 -39,9193 2779,82 -0,01436 320 97815 76

~7815 76 97815 77

320 97815 77 320 978151 78 320 97815 78 320 97815 79 =;: 97815 79 3 97815 80 320 978VO 81 0,300105 76119 -21696 2,1584504 -39,5001 2800,77 -0,0141 320 978151 81 320 97815 81

15

experiment 14C

63 97815 82 320 97815 82 320 97815 83 320 97815 83 320 97815 ! 320 97815 320 99350 85 320 99350 85 82,8 0,322083 76027 -23323 2,1357263 -41,9815 2829,41 -0,01484 320 99350

~ 320 99350 rn=99350 •

99350 320 99733 88 320 99733 88 320 99733 89 320 99733 89 320 99733 90 320 997331 90 84 0,336472 76027 -23707 2,1207658 -42,3591 2850,31 -0,01486 320 99733 91 320 99733 91 320 99733 92 320 99733 92 320 99733 93 64 99733 93

320 99733 94 320 99733 94 320 99733 95 320 99733 95 85,2 0,350657 76003 -23730 2,1060027 -42,0964 2870,03 -0,01467

~9733 96 9733 96

320 99733 97 320 99733 97 65 99733 98

320 99733 98 320 99733 99 319 99733 99 320 99733 100 320 99733 100 86 0,360003 75945 -23788 2,096347 -41,9993 2881,49 -0,01458 66 99733 101

319 99733 101 320 99733 102 319 99733 102 320 99733 103 319 99733 103 320 104720 104 320 104720 104 65 104720 105 65 104720 105 t 87,2 0,37386 15433 -89287 2,200974 -148,084 623,346 -0,23756 45 104720 106

16

experiment 14C

programmed values p [bar] F [N] reached values preal [bar Freal [N] step 1 o 50000 step 1 17 56771

2 135 54654 2 163 56771 3 161 66173 3 212 66744 4 178 74132 4 241 75567 5 190 80445 5 260 83239 6 199 85785 6 260 83239 7 207 90474 7 288 90527 8 213 94692 8 288 90527 9 218 98554 9 303 95130

10 223 102136 10 313 98199 11 227 105589 11 320 104720 12 230 108654 12 320 104720 13 218 98554 13 65 104720 14 178 74132 14 65 104720

programmed vs. real pressure in expo 14C

350

300

250

200 'i:' J .... Co

1~preal [bar] I

150

100

65 50

0 0 2 4 6 8 10 12 14

step

17

350

300

250

200

150

100

50

experiment 14C

pressure and force vs. steps in expo 14C

20 39 58 77 96 115134153172191210229248267286305324343

step

18

120000

100000

80000

40000

20000

o

90

85

80

E oS ...

75 (I) ... (I)

E ca :s

70

65

60 o 20

experiment 14C

alpha and diameter during the process 14C.exp

40 60

time [5]

80

19

100

o

-0,1

-0,2

-0,3

-0,4

-0,5

-0,6

-0,7

-0,8 120

CIS --+-D [mm] J:. Q.

alpha iii ..

experiment 12

BURSTED!!!!! programmed values p [bar] F [N] reached values preal [bar Freal [N] ste 1 0 50000 ep

2 140 52100 1 16 51784 2 170 5 ----I

3 166 63000 3 220 6597 4 183 70600 4 248 71731 5 195 76600 5 268 78636 6 204 81700 6 268 78636 7 212 86200 7 294 82855 8 219 90100 8 306 88609 9 224 93800 9 315 90143

10 229 97200 10 323 92829 N 11 232 100400 11 323 N92829

real pressure vs. programmed pressure in expo 12

350

300

250

'i:' 200

l a. 150

100

50

2 4 6

step

8

20

10

- preal [bar] -+-p[bar]

12

experiment 12


350 120000

300 100000

250 80000

200 'i:'

Ii: e. 60000 c:&. LI.

150

40000 100

50 20000

0 0 27 53 79105131157183209235261287313339365391417443469

step

21

experiment 11

programmed values p [bar1 F [N] reached values preal [bar] Freal [N] step 1 o 50000 step 1 17 56771

2 135 54654 2 163 56771 3 161 66173 3 212 66744 4 178 74132 4 241 75567 5 190 80445 5 260 83239 6 199 85785 6 260 83239 7 207 90474 7 288 90527 8 213 94692 8 288 90527 9 218 98554 9 303 95130

10 223 102136 10 313 98199 11 227 105589 11 320 104720 12 230 108654 12 320 104720 13 218 98554 13 65 104720 14 178 74132 14 65 104720

programmed vs. real pressure in expo 11

350

300

250

200 'i:"

e Q.

150

100

50

step

22

experiment 11


350 120000

300 100000

250 80000

200 'l:"

~ ftI 60000 ;9.

a. u. 150

40000 100

50 20000

0 0 20 3958 n 96 115134153172191 210229248 267 286305 324

step

23

experiment 10

programmed values p [bar] F [N] reached values preal [bar] Freal [N] step 1 o 50000 step 1 11 51017

2 136 54600 2 170 55620 3 162 66200 3 215 65997 4 178 74100 4 235 72498 5 190 80400 5 258 80554 6 200 85800 6 276 86691 7 207 90500 7 275 86691 8 213 94700 8 295 90143 9 218 98600 9 304 93979

10 223 102100 10 313 97432 11 227 105000 11 320 102035 12 230 108600 12 327 107405 13 178 74100 13 48 107405 14 136 54600 14 41 60991


350

300

250

200 -.:'

! Co

150

100

50

0 0 2 4 6 8 10 12

step

24

14

"""-p[bar] _preal (bar]

136

41

350

300

250

200 ';:" IS

:2. g,

150

100

50

o

experiment 10

pressure and force vs. step in exp.10

1 17 33 49 65 81 97113129145161177193209225241257273

step

25

120000

100000

80000

60000 ~ u..

40000

20000

o

programmed values p [bar] mep 1

2 3 4 5 6 7 8 9

10 11

N 12

350

300

250

200 'i:" III r:e. Q.

150

100

50

2

experiment 9

F [N] reached values real [bar Freal [N] o 50000 step 1 11 51017

136 54600 2 170 55620 162 66200 3 213 67128 178 74100 4 237 75183 190 80400 5 257 80554 200 85800 6 275 89760 207 90500 7 275 89760 213 94700 8 294 90143 218 98600 9 303 95130 223 102100 10 313 97048 227 105000 11 320 102418 230 108600 12 325 N102418


4 6

step

26

8 10

230

"""-p[barl : _ preal [bar)

12

experiment 9

pressure and force vs. step in expo 9

350 120000

300 100000

250 80000

200 'C" g l 60000 CI. II.

150

40000 100

50 20000

0 0 18 35 52 69 86 103120 137154171188205 222239256273290

step

27

experiment 8

programmed values p [bar] . F [N] reached values preal [bar] Freal [N] step 1 o 50000 step 1 11 51017

2 136 54600 2 165 52935 3 162 66200 3 214 65594 4 178 74100 4 239 75183 5 190 80400 5 260 82472 6 200 85800 6 261 82472 7 207 90500 7 288 86307 8 213 94700 8 297 92061 9 218 98600 9 305 93979

N 10 223 102100 10 314 N96664


350

314 300

250

223

200 'l:"

! -+-p[barl

- preal [bar] CI.

150

100

50

0 0 2 4 6 8 10

step

28

350

300

250

200 "i:'

e. c:a. 150

100

50

experiment 8


14 27 40 53 66 79 92105118131144157170183196209222

step

29

100000

90000

80000

70000

80000

40000

30000

20000

10000

o

experiment 6

BURSTED!!! programmed values p [bar] F [N] reached values preal [bar Freal [N] step 1 0 45000 step 1 17 50250

2 143 49400 2 174 54086 3 170 60000 3 227 63676 4 187 67000 4 255 69046 5 200 72500 5 255 69046 6 210 77300 6 295 82855 7 217 81500 7 295 82855 8 224 85300 8 304 82855

N 9 229 88700 9 325 N80937


350

325

300

250

229

200 0;:' 1\1 .Q

.-+-p[bar) .... r::a. i --preal (bar]

150

100

50

step

30

350

300

250

'i:' 200

"' e. a-

150

100

experiment6


1 14 27 40 53 66 79 92 105118131144157170183196209222

step

31

100000

90000

80000

70000

60000

50000 ~ u..

40000

30000

20000

10000

o

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